0=-x^2+20x-11

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Solution for 0=-x^2+20x-11 equation:


Simplifying
0 = -1x2 + 20x + -11

Reorder the terms:
0 = -11 + 20x + -1x2

Solving
0 = -11 + 20x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 11 = 11
11 + -20x + x2 = -11 + 20x + -1x2 + 11 + -20x + x2

Reorder the terms:
11 + -20x + x2 = -11 + 11 + 20x + -20x + -1x2 + x2

Combine like terms: -11 + 11 = 0
11 + -20x + x2 = 0 + 20x + -20x + -1x2 + x2
11 + -20x + x2 = 20x + -20x + -1x2 + x2

Combine like terms: 20x + -20x = 0
11 + -20x + x2 = 0 + -1x2 + x2
11 + -20x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
11 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -20x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -20x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -20x + x2 = 0 + -11
-20x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-20x + x2 = -11

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -11 + 100

Reorder the terms:
100 + -20x + x2 = -11 + 100

Combine like terms: -11 + 100 = 89
100 + -20x + x2 = 89

Factor a perfect square on the left side:
(x + -10)(x + -10) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + -10) equal to 9.433981132 and -9.433981132.

Subproblem 1

x + -10 = 9.433981132 Simplifying x + -10 = 9.433981132 Reorder the terms: -10 + x = 9.433981132 Solving -10 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.433981132 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.433981132 + 10 x = 9.433981132 + 10 Combine like terms: 9.433981132 + 10 = 19.433981132 x = 19.433981132 Simplifying x = 19.433981132

Subproblem 2

x + -10 = -9.433981132 Simplifying x + -10 = -9.433981132 Reorder the terms: -10 + x = -9.433981132 Solving -10 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.433981132 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.433981132 + 10 x = -9.433981132 + 10 Combine like terms: -9.433981132 + 10 = 0.566018868 x = 0.566018868 Simplifying x = 0.566018868

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.433981132, 0.566018868}

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